New approaches are required in the agricultural sector to keep pace with the ever-growing demand for food in the context of climate change and resource deterioration and avoiding further negative impact on the environment. Nonthermal plasma is an environmentally-friendly technology which could make a difference in future agricultural production. This review intends to introduce the topic of plasma agriculture to a broad audience by describing in detail various plasma sources with potential for agricultural applications, as well as the effects of plasma exposure of seeds, both at the macroscopic scale, and concerning the intimate mechanisms occurring inside the plant. Examples meant to illustrate the plasma effect on seeds and plants have been selected among extensively investigated species, such as cereals and legumes, as well as among a few species that are less often reported in literature, such as medicinal plants and woody plants. Generally, the main effects for all types of seeds consist in increased germination, higher plant yield, seed decontamination, and sometimes higher tolerance to various stress factors. These effects are due to the physical and chemical plasma interaction with seeds followed by the response of cell mechanisms, which are addressed in detail in the paper. Finally, a few crucial aspects regarding the practical application of nonthermal plasma in agriculture are discussed to illustrate the challenges and perspective of such treatments.